Find the ratio of the areas of triangles ABC and KMN if AB = 6, BC = 10, AC = 14, KM = 9, MN = 15, NK = 21.
| November 24, 2020 | education
The ratio of the areas of two similar triangles is equal to the coefficient of similarity of triangles (k) squared.
Then you can derive the relations:
S (ABC) / S (KMN) = k ^ 2
k = AB / MN = AC / MK = BC / NK = P (ABC) / P (KMN)
We get:
S (ABC) / S (KMN) = (AB / MN) ^ 2
S (ABC) / S (KMN) = 4/9
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